I definitely don't want to make it cave worthy, and don't have any hatred or anything towards those who do, but WE'RE the ones that eliminated their natural predators. Sounds more like a We problem than a Them problem. Also, if you REALLY wanted to get in to a debate, you could argue that humans are the most over-populated animals in the world. But few are legitimately suggesting human hunts to control it.
We're a capitalistic society. We could hold it in an arena, televise it, get sponsors. If done right, I bet someone could even make a movie about it.